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A coin made of alloy of aluminum and silver measures 2 x 15
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27 Nov 2007, 19:14

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A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is 2 mm thick and its diameter is 15 mm). The weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver. What will be the weight of the coin measuring 1 x 30 mm made of pure aluminum if silver is twice heavier than aluminium?

(A) 36 grams
(B) 40 grams
(C) 42 grams
(D) 48 grams
(E) 50 grams

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27 Nov 2007, 20:40

eyunni wrote:

A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is 2 mm thick and its diameter is 15 mm). The weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver. What will be the weight of the coin measuring 1 x 30 mm made of pure aluminum if silver is twice heavier than aluminium?

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27 Nov 2007, 21:08

eyunni wrote:

A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is 2 mm thick and its diameter is 15 mm). The weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver. What will be the weight of the coin measuring 1 x 30 mm made of pure aluminum if silver is twice heavier than aluminium?

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A coin is essentially a very flat cylinder.
Volume of a cylinder = Area of circle * Height

Volume of 1st coin
V = pi* (r^2) * H
V = pi * 56.25 * 2
V = 112.5pi

Volume of 2nd coin
V = pi* (r^2) * H
V = pi 225
Thus, the volume of the second coin is twice the first coin.

A + S = 30 grams
A + 2A = 30
A = 10 grams

Since the second coin is all aluminum, we can assume the first coin is all aluminum and that it would weigh 20 grams. Since the second coin is twice the weight of the first coin, the second coin is 40 grams.

Re: A coin made of alloy of aluminum and silver measures 2 x 15
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02 Oct 2017, 01:08

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